financial accounting and accounting standards · after studying this chapter, you should be able...
TRANSCRIPT
6-1
6-2
PREVIEW OF CHAPTER
Intermediate Accounting
IFRS 2nd Edition
Kieso, Weygandt, and Warfield
6
6-3
1. Identify accounting topics where the
time value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-4
BASIC TIME VALUE CONCEPTS
A relationship between time and money.
A dollar received today is worth more than a dollar
promised at some time in the future.
Time Value of Money
When deciding among investment or
borrowing alternatives, it is essential to be
able to compare today’s dollar and
tomorrow’s dollar on the same footing—to
“compare apples to apples.”
LO 1
6-5
1. Notes
2. Leases
3. Pensions and Other
Postretirement
Benefits
4. Long-Term Assets
Applications of Time Value Concepts:
5. Shared-Based
Compensation
6. Business Combinations
7. Disclosures
8. Environmental Liabilities
BASIC TIME VALUE CONCEPTS
LO 1
6-6
Payment for the use of money.
Excess cash received or repaid over the amount lent
or borrowed (principal).
The Nature of Interest
BASIC TIME VALUE CONCEPTS
LO 1
6-7
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and
compound interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-8
Interest computed on the principal only.
Simple Interest
Illustration: Barstow Electric Inc. borrows $10,000 for 3 years
at a simple interest rate of 8% per year. Compute the total
interest to be paid for 1 year.
Interest = p x i x n
= $10,000 x .08 x 1
= $800
Annual
Interest
BASIC TIME VALUE CONCEPTS
LO 2
6-9
Interest computed on the principal only.
Simple Interest
Illustration: Barstow Electric Inc. borrows $10,000 for 3 years
at a simple interest rate of 8% per year. Compute the total
interest to be paid for 3 years.
Interest = p x i x n
= $10,000 x .08 x 3
= $2,400
Total
Interest
BASIC TIME VALUE CONCEPTS
LO 2
6-10
Simple Interest
Interest = p x i x n
= $10,000 x .08 x 3/12
= $200
Interest computed on the principal only.
Illustration: If Barstow borrows $10,000 for 3 months at a 8%
per year, the interest is computed as follows.
Partial
Year
BASIC TIME VALUE CONCEPTS
LO 2
6-11
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest
tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-12
Compound Interest
Computes interest on
► principal and
► interest earned that has not been paid or withdrawn.
Typical interest computation applied in business
situations.
BASIC TIME VALUE CONCEPTS
LO 3
6-13
Illustration: Tomalczyk Company deposits $10,000 in the Last National
Bank, where it will earn simple interest of 9% per year. It deposits another
$10,000 in the First State Bank, where it will earn compound interest of
9% per year compounded annually. In both cases, Tomalczyk will not
withdraw any interest until 3 years from the date of deposit.
Year 1 $10,000.00 x 9% $ 900.00 $ 10,900.00
Year 2 $10,900.00 x 9% $ 981.00 $ 11,881.00
Year 3 $11,881.00 x 9% $1,069.29 $ 12,950.29
ILLUSTRATION 6-1
Simple vs. Compound Interest
Compound Interest
LO 3
6-14
The continuing debate by
governments as to how to provide
retirement benefits to their citizens
serves as a great context to illustrate
the power of compounding. One
proposed idea is for the government to
give $1,000 to every citizen at birth.
This gift would be deposited in an
account that would earn interest tax-
free until the citizen retires. Assuming
the account earns a 5% annual return
until retirement at age 65, the $1,000
would grow to $23,839. With monthly
compounding, the $1,000 deposited at
birth would grow to $25,617.
WHAT’S YOUR PRINCIPLE A PRETTY GOOD START
Why start so early? If the government
waited until age 18 to deposit the
money, it would grow to only $9,906
with annual compounding. That is,
reducing the time invested by a third
results in more than a 50% reduction
in retirement money. This example
illustrates the importance of starting
early when the power of compounding
is involved.
LO 3
6-15
Table 6-1 - Future Value of 1
Table 6-2 - Present Value of 1
Table 6-3 - Future Value of an Ordinary Annuity of 1
Table 6-4 - Present Value of an Ordinary Annuity of 1
Table 6-5 - Present Value of an Annuity Due of 1
Compound Interest Tables
Number of Periods = number of years x the number of compounding
periods per year.
Compounding Period Interest Rate = annual rate divided by the
number of compounding periods per year.
BASIC TIME VALUE CONCEPTS
LO 3
6-16
How much principal plus interest a dollar accumulates to at the end of
each of five periods, at three different rates of compound interest.
ILLUSTRATION 6-2
Excerpt from Table 6-1
Compound Interest Tables
FUTURE VALUE OF 1 AT COMPOUND INTEREST
(Excerpt From Table 6-1)
BASIC TIME VALUE CONCEPTS
LO 3
6-17
Formula to determine the future value factor (FVF) for 1:
Where:
Compound Interest Tables
FVFn,i = future value factor for n periods at i interest
n = number of periods
i = rate of interest for a single period
BASIC TIME VALUE CONCEPTS
LO 3
6-18
To illustrate the use of interest tables to calculate compound
amounts, Illustration 6-3 shows the future value to which 1
accumulates assuming an interest rate of 9%. ILLUSTRATION 6-3
Accumulation of
Compound Amounts
Compound Interest Tables
BASIC TIME VALUE CONCEPTS
LO 3
6-19
Number of years X number of compounding periods per year =
Number of periods ILLUSTRATION 6-4
Frequency of Compounding
Compound Interest Tables
BASIC TIME VALUE CONCEPTS
LO 3
6-20
A 9% annual interest compounded daily provides a 9.42% yield.
Effective Yield for a $10,000 investment. ILLUSTRATION 6-5
Comparison of Different
Compounding Periods
Compound Interest Tables
BASIC TIME VALUE CONCEPTS
LO 3
6-21
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to
solving interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-22
Rate of Interest
Number of Time Periods
Fundamental Variables
ILLUSTRATION 6-6
Basic Time Diagram
Future Value
Present Value
BASIC TIME VALUE CONCEPTS
LO 4
6-23
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1
problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-24
SINGLE-SUM PROBLEMS
Unknown Future Value
Two Categories
ILLUSTRATION 6-6
Basic Time Diagram
Unknown Present Value
LO 5
6-25
Value at a future date of a given amount invested, assuming
compound interest.
FV = future value
PV = present value (principal or single sum)
= future value factor for n periods at i interest FVF n,i
Where:
Future Value of a Single Sum
SINGLE-SUM PROBLEMS
LO 5
6-26
Future Value of a Single Sum
Illustration: Bruegger Co. wants to determine the future
value of €50,000 invested for 5 years compounded annually at
an interest rate of 11%.
= €84,253
ILLUSTRATION 6-7
Future Value Time
Diagram (n = 5, i = 11%)
LO 5
6-27
What table
do we use?
Future Value of a Single Sum
Illustration: Bruegger Co. wants to determine the future
value of €50,000 invested for 5 years compounded annually at
an interest rate of 11%.
Alternate
Calculation
ILLUSTRATION 6-7
Future Value Time
Diagram (n = 5, i = 11%)
LO 5
6-28
What factor do we use?
€50,000
Present Value Factor Future Value
x 1.68506 = €84,253
i=11%
n=5
Future Value of a Single Sum Alternate
Calculation
LO 5
6-29
Illustration: Shanghai Electric Power (CHN) deposited
¥250 million in an escrow account with Industrial and Commercial
Bank of China (CHN) at the beginning of 2015 as a commitment
toward a power plant to be completed December 31, 2018. How
much will the company have on deposit at the end of 4 years if
interest is 10%, compounded semiannually?
What table do we use?
Future Value of a Single Sum
ILLUSTRATION 6-8
Future Value Time
Diagram (n = 8, i = 5%)
LO 5
6-30
Present Value Factor Future Value
¥250,000,000 x 1.47746 = ¥369,365,000
i=5%
n=8
Future Value of a Single Sum
LO 5
6-31
Present Value of a Single Sum
SINGLE-SUM PROBLEMS
Amount needed to invest now, to produce a known future value.
Formula to determine the present value factor for 1:
Where:
PVFn,i = present value factor for n periods at i interest
n = number of periods
i = rate of interest for a single period
LO 5
6-32
Assuming an interest rate of 9%, the present value of 1
discounted for three different periods is as shown in Illustration
6-10. ILLUSTRATION 6-10
Present Value of 1
Discounted at 9% for
Three Periods
Present Value of a Single Sum
LO 5
6-33
ILLUSTRATION 6-9
Excerpt from Table 6-2
Illustration 6-9 shows the “present value of 1 table” for five
different periods at three different rates of interest.
Present Value of a Single Sum
LO 5
6-34
Amount needed to invest now, to produce a known future value.
Where:
FV = future value
PV = present value
= present value factor for n periods at i interest PVF n,i
LO 5
Present Value of a Single Sum
6-35
Illustration: What is the present value of €84,253 to be
received or paid in 5 years discounted at 11% compounded
annually?
Present Value of a Single Sum
= €50,000
ILLUSTRATION 6-11
Present Value Time
Diagram (n = 5, i = 11%)
LO 5
6-36
What table do we use?
Present Value of a Single Sum
Illustration: What is the present value of €84,253 to be
received or paid in 5 years discounted at 11% compounded
annually?
Alternate
Calculation
ILLUSTRATION 6-11
Present Value Time
Diagram (n = 5, i = 11%)
LO 5
6-37
€84,253
Future Value Factor Present Value
x .59345 = €50,000
What factor?
i=11%
n=5
Present Value of a Single Sum
LO 5
6-38
Illustration: Assume that your rich uncle decides to give you
$2,000 for a vacation when you graduate from college 3 years from
now. He proposes to finance the trip by investing a sum of money
now at 8% compound interest that will provide you with $2,000
upon your graduation. The only conditions are that you graduate
and that you tell him how much to invest now.
What table do we use?
ILLUSTRATION 6-12
Present Value Time
Diagram (n = 3, i = 8%)
Present Value of a Single Sum
LO 5
6-39
$2,000
Future Value Factor Present Value
x .79383 = $1,587.66
What factor?
i=8%
n=3
Present Value of a Single Sum
LO 5
6-40
Solving for Other Unknowns
Example—Computation of the Number of Periods
The Village of Somonauk wants to accumulate $70,000 for the
construction of a veterans monument in the town square. At the
beginning of the current year, the Village deposited $47,811 in a
memorial fund that earns 10% interest compounded annually. How
many years will it take to accumulate $70,000 in the memorial
fund? ILLUSTRATION 6-13
SINGLE-SUM PROBLEMS
LO 5
6-41
Example—Computation of the Number of Periods
ILLUSTRATION 6-14
Using the future value factor of
1.46410, refer to Table 6-1 and read
down the 10% column to find that
factor in the 4-period row.
Solving for Other Unknowns
LO 5
6-42
Example—Computation of the Number of Periods
ILLUSTRATION 6-14
Using the present value factor of
.68301, refer to Table 6-2 and read
down the 10% column to find that
factor in the 4-period row.
Solving for Other Unknowns
LO 5
6-43
ILLUSTRATION 6-15
Advanced Design, Inc. needs €1,409,870 for basic research 5
years from now. The company currently has €800,000 to invest
for that purpose. At what rate of interest must it invest the
€800,000 to fund basic research projects of €1,409,870, 5 years
from now?
Example—Computation of the Interest Rate
Solving for Other Unknowns
LO 5
6-44
ILLUSTRATION 6-16
Using the future value factor of
1.76234, refer to Table 6-1 and
read across the 5-period row to
find the factor.
Example—Computation of the Interest Rate
Solving for Other Unknowns
LO 5
6-45
Using the present value factor of
.56743, refer to Table 6-2 and
read across the 5-period row to
find the factor.
Example—Computation of the Interest Rate
Solving for Other Unknowns
ILLUSTRATION 6-16
LO 5
6-46
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and
annuity due problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-47
(1) Periodic payments or receipts (called rents) of the
same amount,
(2) Same-length interval between such rents, and
(3) Compounding of interest once each interval.
Annuity requires:
Ordinary Annuity - rents occur at the end of each period.
Annuity Due - rents occur at the beginning of each period.
Two
Types
ANNUITIES
LO 6
6-48
Future Value of an Ordinary Annuity
Rents occur at the end of each period.
No interest during 1st period.
0 1
Present Value
2 3 4 5 6 7 8
$20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000
Future Value
ANNUITIES
LO 6
6-49
Illustration: Assume that $1 is deposited at the end of each
of 5 years (an ordinary annuity) and earns 12% interest
compounded annually. Illustration 6-17 shows the
computation of the future value, using the “future value of 1”
table (Table 6-1) for each of the five $1 rents. ILLUSTRATION 6-17
Future Value of an Ordinary Annuity
LO 6
6-50
Illustration 6-18 provides an excerpt from the “future value of an
ordinary annuity of 1” table. ILLUSTRATION 6-18
Future Value of an Ordinary Annuity
LO 6
*Note that this annuity table factor is the same as the sum of
the future values of 1 factors shown in Illustration 6-17.
6-51
R = periodic rent
FVF-OA = future value factor of an ordinary annuity
i = rate of interest per period
n = number of compounding periods
A formula provides a more efficient way of expressing the
future value of an ordinary annuity of 1.
Where:
n,i
Future Value of an Ordinary Annuity
LO 6
6-52
Illustration: What is the future value of five $5,000 deposits
made at the end of each of the next 5 years, earning interest
of 12%?
= $31,764.25
ILLUSTRATION 6-19
Time Diagram for Future
Value of Ordinary
Annuity (n = 5, i = 12%)
Future Value of an Ordinary Annuity
LO 6
6-53
Illustration: What is the future value of five $5,000 deposits
made at the end of each of the next 5 years, earning interest
of 12%?
What table do we use?
Future Value of an Ordinary Annuity Alternate
Calculation
ILLUSTRATION 6-19
LO 6
6-54
$5,000
Deposits Factor Future Value
x 6.35285 = $31,764
What factor?
i=12%
n=5
Future Value of an Ordinary Annuity
LO 6
6-55
Illustration: Gomez Inc. will deposit $30,000 in a 12% fund at
the end of each year for 8 years beginning December 31, 2014.
What amount will be in the fund immediately after the last
deposit?
0 1
Present Value
What table do we use?
2 3 4 5 6 7 8
$30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000
Future Value
Future Value of an Ordinary Annuity
LO 6
6-56
Deposit Factor Future Value
$30,000 x 12.29969 = $368,991
i=12%
n=8
Future Value of an Ordinary Annuity
LO 6
6-57
Future Value of an Annuity Due
Rents occur at the beginning of each period.
Interest will accumulate during 1st period.
Annuity due has one more interest period than ordinary
annuity.
Factor = multiply future value of an ordinary annuity factor by 1
plus the interest rate.
0 1 2 3 4 5 6 7 8
20,000 20,000 20,000 20,000 20,000 20,000 20,000 $20,000
Future Value
ANNUITIES
LO 6
6-58
ILLUSTRATION 6-21
Comparison of Ordinary Annuity with an Annuity Due
Future Value of an Annuity Due
LO 6
6-59
Illustration: Assume that you plan to accumulate CHF14,000 for a
down payment on a condominium apartment 5 years from now. For
the next 5 years, you earn an annual return of 8% compounded
semiannually. How much should you deposit at the end of each 6-
month period?
R = CHF1,166.07
ILLUSTRATION 6-24
Computation of Rent
Future Value of an Annuity Due
LO 6
6-60
Computation of Rent ILLUSTRATION 6-24
CHF14,000 = CHF1,166.07
12.00611
Future Value of an Annuity Due Alternate
Calculation
LO 6
6-61
Illustration: Suppose that a company’s goal is to accumulate
$117,332 by making periodic deposits of $20,000 at the end of each
year, which will earn 8% compounded annually while accumulating.
How many deposits must it make?
ILLUSTRATION 6-25
Computation of Number of Periodic Rents
5.86660
Future Value of an Annuity Due
LO 6
6-62
Illustration: Mr. Goodwrench deposits $2,500 today in a savings
account that earns 9% interest. He plans to deposit $2,500 every
year for a total of 30 years. How much cash will Mr. Goodwrench
accumulate in his retirement savings account, when he retires in 30
years?
ILLUSTRATION 6-27
Computation of Future Value
Future Value of an Annuity Due
LO 6
6-63
Illustration: Bayou Inc. will deposit $20,000 in a 12% fund at
the beginning of each year for 8 years beginning January 1,
Year 1. What amount will be in the fund at the end of Year 8?
0 1
Present Value
What table do we use?
2 3 4 5 6 7 8
$20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000
Future Value
Future Value of an Annuity Due
LO 6
6-64
Deposit Factor Future Value
12.29969 x 1.12 = 13.775652
i=12%
n=8
$20,000 x 13.775652 = $275,513
Future Value of an Annuity Due
LO 6
6-65
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and
annuity due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-66
Present Value of an Ordinary Annuity
Present value of a series of equal amounts to be
withdrawn or received at equal intervals.
Periodic rents occur at the end of the period.
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . . 100,000
ANNUITIES
LO 7
6-67
Illustration: Assume that $1 is to be received at the end of
each of 5 periods, as separate amounts, and earns 12%
interest compounded annually.
Present Value of an Ordinary Annuity
ILLUSTRATION 6-28
Solving for the Present
Value of an Ordinary Annuity
LO 7
6-68
A formula provides a more efficient way of expressing the
present value of an ordinary annuity of 1.
Where:
Present Value of an Ordinary Annuity
LO 7
6-69
Illustration: What is the present value of rental receipts of
$6,000 each, to be received at the end of each of the next 5
years when discounted at 12%? ILLUSTRATION 6-30
Present Value of an Ordinary Annuity
LO 7
6-70
Illustration: Jaime Yuen wins $2,000,000 in the state lottery.
She will be paid $100,000 at the end of each year for the next
20 years. How much has she actually won? Assume an
appropriate interest rate of 8%.
0 1
Present Value
What table do we use?
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . . 100,000
Present Value of an Ordinary Annuity
LO 7
6-71
$100,000
Receipts Factor Present Value
x 9.81815 = $981,815
i=8%
n=20
Present Value of an Ordinary Annuity
LO 7
6-72
Time value of money concepts also can be
relevant to public policy debates. For example,
many governments must evaluate the financial
cost-benefit of selling to a private operator the
future cash flows associated with government-run
services, such as toll roads and bridges. In these
cases, the policymaker must estimate the present
value of the future cash flows in determining the
price for selling the rights. In another example,
some governmental entities had to determine how
to receive the payments from tobacco companies
as settlement for a national lawsuit against the
companies for the healthcare costs of smoking. In
one situation, a governmental entity was due to
collect 25 years of payments totaling $5.6 billion.
The government could wait to collect the
payments, or it could sell the payments to an
investment bank (a process called securitization).
If it were to sell the payments, it would receive a
lump-sum payment today of $1.26 billion. Is this a
good deal for this governmental entity? Assuming
a discount rate of 8% and that the payments will
be received in
WHAT’S YOUR PRINCIPLE UP IN SMOKE
equal amounts (e.g., an annuity), the present
value of the tobacco payment is:
$5.6 billion ÷ 25 = $224 million
$224 million X 10.67478* = $2.39 billion
*PV-OA (i = 8%, n = 25)
Why would the government be willing to take just
$1.26 billion today for an annuity whose present
value is almost twice that amount? One reason is
that the governmental entity was facing a hole in
its budget that could be plugged in part by the
lump-sum payment. Also, some believed that the
risk of not getting paid by the tobacco companies
in the future makes it prudent to get the money
earlier. If this latter reason has merit, then the
present value computation above should have
been based on a higher interest rate. Assuming a
discount rate of 15%, the present value of the
annuity is $1.448 billion ($5.6 billion ÷ 25 = $224
million; $224 million x 6.46415), which is much
closer to the lump-sum payment offered to the
governmental entity.
LO 7
6-73
Present Value of an Annuity Due
Present value of a series of equal amounts to be
withdrawn or received at equal intervals.
Periodic rents occur at the beginning of the period.
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . . 100,000
ANNUITIES
LO 7
6-74
ILLUSTRATION 6-31
Comparison of Ordinary Annuity with an Annuity Due
Present Value of an Annuity Due
LO 7
6-75
Illustration: Space Odyssey, Inc., rents a communications
satellite for 4 years with annual rental payments of $4.8 million
to be made at the beginning of each year. If the relevant
annual interest rate is 11%, what is the present value of the
rental obligations? ILLUSTRATION 6-33
Computation of Present
Value of an Annuity Due
Present Value of an Annuity Due
LO 7
6-76
0 1
Present Value
What table do we use?
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . . 100,000
Present Value of Annuity Problems
Illustration: Jaime Yuen wins $2,000,000 in the state lottery.
She will be paid $100,000 at the beginning of each year for the
next 20 years. How much has she actually won? Assume an
appropriate interest rate of 8%.
LO 7
6-77
$100,000
Receipts Factor Present Value
x 10.60360 = $1,060,360
i=8%
n=20
Present Value of Annuity Problems
LO 7
6-78
Illustration: Assume you receive a statement from MasterCard with
a balance due of €528.77. You may pay it off in 12 equal monthly
payments of €50 each, with the first payment due one month from
now. What rate of interest would you be paying?
Computation of the Interest Rate
Referring to Table 6-4 and reading across the 12-period row, you find 10.57534 in
the 2% column. Since 2% is a monthly rate, the nominal annual rate of interest is
24% (12 x 2%). The effective annual rate is 26.82413% [(1 + .02) - 1]. 12
Present Value of Annuity Problems
LO 7
6-79
Illustration: Juan and Marcia Perez have saved $36,000 to finance
their daughter Maria’s college education. They deposited the money
in the Santos Bank, where it earns 4% interest compounded
semiannually. What equal amounts can their daughter withdraw at
the end of every 6 months during her 4 college years, without
exhausting the fund?
Computation of a Periodic Rent
12
Present Value of Annuity Problems
LO 7
6-80
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related
to deferred annuities and bonds.
9. Apply expected cash flows to present value
measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-81
Rents begin after a specified number of periods.
Future Value of a Deferred Annuity - Calculation same
as the future value of an annuity not deferred.
Present Value of a Deferred Annuity - Must recognize
the interest that accrues during the deferral period.
0 1 2 3 4 19 20
100,000 100,000 100,000
. . . . .
Future Value Present Value
Deferred Annuities
MORE COMPLEX SITUATIONS
LO 8
6-82
Future Value of Deferred Annuity
MORE COMPLEX SITUATIONS
Illustration: Sutton Corporation plans to purchase a land site in 6
years for the construction of its new corporate headquarters. Sutton
budgets deposits of $80,000 on which it expects to earn 5% annually,
only at the end of the fourth, fifth, and sixth periods. What future value
will Sutton have accumulated at the end of the sixth year?
ILLUSTRATION 6-37
LO 8
6-83
Present Value of Deferred Annuity
MORE COMPLEX SITUATIONS
Illustration: Bob Bender has developed and copyrighted tutorial
software for students in advanced accounting. He agrees to sell the
copyright to Campus Micro Systems for 6 annual payments of $5,000
each. The payments will begin 5 years from today. Given an annual
interest rate of 8%, what is the present value of the 6 payments?
Two options are available to solve this problem.
LO 8
6-84
Present Value of Deferred Annuity
ILLUSTRATION 6-38
ILLUSTRATION 6-39 Use Table 6-4
LO 8
6-85
Present Value of Deferred Annuity
Use Table 6-2 and 6-4
LO 8
6-86
Two Cash Flows:
Periodic interest payments (annuity).
Principal paid at maturity (single-sum).
0 1 2 3 4 9 10
140,000 140,000 140,000 $140,000
. . . . . 140,000 140,000
2,000,000
Valuation of Long-Term Bonds
MORE COMPLEX SITUATIONS
LO 8
6-87
BE6-15: Wong Inc. issues HK$2,000,000 of 7% bonds due in
10 years with interest payable at year-end. The current market
rate of interest for bonds of similar risk is 8%. What amount will
Wong receive when it issues the bonds?
0 1
Present Value
2 3 4 9 10
140,000 140,000 140,000 HK$140,000
. . . . . 140,000 2,140,000
Valuation of Long-Term Bonds
LO 8
6-88
HK$140,000 x 6.71008 = HK$939,411
Interest Payment Factor Present Value
PV of Interest
i=8%
n=10
Valuation of Long-Term Bonds
LO 8
6-89
HK$2,000,000 x .46319 = HK$926,380
Principal Factor Present Value
PV of Principal
Valuation of Long-Term Bonds i=8%
n=10
LO 8
6-90
1. Identify accounting topics where the time
value of money is relevant.
2. Distinguish between simple and compound
interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving
interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due
problems.
7. Solve present value of ordinary and annuity
due problems.
8. Solve present value problems related to
deferred annuities and bonds.
9. Apply expected cash flows to present
value measurement.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money 6 LEARNING OBJECTIVES
6-91
Instructions: How much should Angela Contreras deposit today in an
account earning 6%, compounded annually, so that she will have enough
money on hand in 2 years to pay for the overhaul?
PRESENT VALUE MEASUREMENT
LO 9
6-92
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